Dependent conditional tail expectation for extreme levels

Yuri Goegebeur, Armelle Guillou and Jing Qin

Stochastic Processes and their Applications, 2024, vol. 171, issue C

Abstract: We consider the estimation of the dependent conditional tail expectation, defined for a random vector (X,Y) with X≥0 as E(X|X>QX(1−p),Y>QY(1−p)), when E(X)<∞, and where QX and QY denote the quantile functions of X and Y, respectively. The distribution of X is assumed to be of Pareto-type while the distribution of Y is kept general. Using extreme-value arguments we introduce an estimator for this risk measure for the situation p≤1/n, where n is the number of available observations, i.e., focus is on estimation with extrapolation. The convergence in distribution of our estimator is established and its finite sample performance is illustrated on a simulation study. The method is then applied on wind gusts data set.

Keywords: Bivariate extreme value statistics; Empirical process; Tail copula; Pareto-type distribution (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104330

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